This paper studies decoupled numerical methods for a mixed Stokes/Darcy model for coupling fluid and porous media flows. A two-level algorithm is proposed and analyzed in Mu and Xu (2007) [10]. We generalize the two-l...
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This paper studies decoupled numerical methods for a mixed Stokes/Darcy model for coupling fluid and porous media flows. A two-level algorithm is proposed and analyzed in Mu and Xu (2007) [10]. We generalize the two-level algorithm to a multilevel algorithm in this paper and present numerical analysis on the error estimates for the multilevel algorithm. The multilevel algorithm solves the mixed Stokes/Darcy system by applying efficient legacy code for single model solvers to solve two decoupled Stokes and Darcy subproblems on all the subsequently refined meshes, except for a much smaller global problem only on a very coarse initial mesh. Numerical experiments are conducted for both the two-level and multilevel algorithms to illustrate their effectiveness and efficiency, and validate the related theoretical analysis. (C) 2011 Elsevier B.V. All rights reserved.
When applying multilevel scheme to solve the graph partitioning problem, shortcomings and limitations exist in the state-of-the-art coarsening schemes depend mainly on finding maximal matchings to obtain the coarse gr...
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ISBN:
(纸本)9783037853849
When applying multilevel scheme to solve the graph partitioning problem, shortcomings and limitations exist in the state-of-the-art coarsening schemes depend mainly on finding maximal matchings to obtain the coarse graphs, which can cause the multilevel algorithms to produce poor-quality solutions. This paper proposes an improved coarsening scheme by improving vertex combining strategy and edge ordering criteria. The new coarsening scheme is more effective in quality, which is proved by both theoretical analysis and experimental results.
A fast algorithm combined with the volume integral equation (VIE) is proposed for analyzing antenna radiation properties in the presence of an arbitrary shaped dielectric radome. The discrete form of the VIE is obtain...
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ISBN:
(纸本)9781457716928
A fast algorithm combined with the volume integral equation (VIE) is proposed for analyzing antenna radiation properties in the presence of an arbitrary shaped dielectric radome. The discrete form of the VIE is obtained using the method of moments (MOM). Evaluation of electromagnetic fields is accelerated using the multilevel volumetric non-uniform grid algorithm (MLVNG). The algorithm is based on phase and amplitude compensation of fields which are produced by a bounded volume of source distribution. The compensated field is band-limited function of its coordinates, which allows sampling it on a sparse non-uniform spherical grid at rates proportional to the source volume. Tight sampling rules are suggested in order to reduce the computational complexity of the field evaluation. The computational complexity of the MLVNG algorithm is demonstrated on representative example.
This paper presents the synergetic use of different evaluation tools, parameterization schemes and search methods on the levels of a multilevel optimization platform to efficiently solve single-and multi-objective com...
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This paper presents the synergetic use of different evaluation tools, parameterization schemes and search methods on the levels of a multilevel optimization platform to efficiently solve single-and multi-objective computationally demanding optimization problems. The platform is formed by a number of levels which concurrently search for optimal solutions, by regularly exchanging promising individual solutions. Each level is associated with a problem-specific evaluation tool with its own accuracy and computational cost, a parameterization scheme which determines the design variables and their mapping to generate individual solutions and a search algorithm which is either a metamodel-assisted evolutionary algorithm or a gradient-based method. The use of the multilevel platform with only one of the aforementioned features changing from level to level was presented in a previous paper by the authors. The present paper shows that the combined use of hierarchical evaluation, hierarchical parameterization and hierarchical search decreases further the computational cost by increasing the efficiency of the optimization method. This is demonstrated on function minimization and aerodynamic shape optimization problems;though only two levels are used herein, this is not a restriction and the optimization platform may accommodate any number of them. (C) 2009 Elsevier B.V. All rights reserved.
In this paper, a new variant of the multilevel algorithm for computing the steady-state solution of a continuous-time Markov chain is proposed. The method is integrated into a symbolic framework, where the CTMC is rep...
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ISBN:
(纸本)9780955301841
In this paper, a new variant of the multilevel algorithm for computing the steady-state solution of a continuous-time Markov chain is proposed. The method is integrated into a symbolic framework, where the CTMC is represented in a compact way using multi-terminal binary decision diagrams (MTBDD). It is shown how to represent the original CTMC and several aggregated chains within the same decision diagram, where particular attention is devoted to the question of how to deal with unreachable states. Some preliminary empirical results are provided which indicate that the method has the potential to solve very large Markov chains in an efficient manner.
Linear ordering problems are combinatorial optimization problems that deal with the minimization of different functionals by finding a suitable permutation of the graph vertices. These problems are widely used and stu...
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Linear ordering problems are combinatorial optimization problems that deal with the minimization of different functionals by finding a suitable permutation of the graph vertices. These problems are widely used and studied in many practical and theoretical applications. In this paper, we present a variety of linear--time algorithms for these problems inspired by the Algebraic Multigrid approach, which is based on weighted-edge contraction. The experimental result for four such problems turned out to be better than every known result in almost all cases, while the short (linear) running time of the algorithms enables testing very large graphs.
A novel method for computing the capacitance matrices of arbitrary shaped three-dimensional geometries is presented. The proposed approach combines a novel nommiform-grid (NG) algorithm for fast evaluation of potentia...
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A novel method for computing the capacitance matrices of arbitrary shaped three-dimensional geometries is presented. The proposed approach combines a novel nommiform-grid (NG) algorithm for fast evaluation of potentials due to given source distributions with an iterative solution of the pertinent integral equations. The NG algorithm is based on the observation that locally the potential produced by a finite size source can be interpolated from its samples at a small number of points of a nonuniform spherical grid. This observation leads to a multilevel algorithm comprising interpolation and aggregation of potentials. The resulting hierarchical algorithm attains an O(N) asymptotic complexity and memory requirements. The computational efficiency is further improved for quasi-planar geometries by the use of adaptive grids.
Many real-world engineering problems can be expressed in terms of partial differential equations an solved by using the finite-element method, which is usually arallelized, i.e. the mesh is divided among several proce...
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Many real-world engineering problems can be expressed in terms of partial differential equations an solved by using the finite-element method, which is usually arallelized, i.e. the mesh is divided among several processors. To achieve high parallel efficiency it is important that the mesh is partitioned in such a way that workloads are well balanced and interprocessor communication is minimized In this paper we present an enhancement of a technique that uses a nature-inspired metaheuristir approach to achieve higher-quality partitions. We present two heuristic mesh-partitioning methods, both of which build on the multiple ant-colony algorithm in order to improve the quality of the mesh partitions. The first method augments the multiple ant-colony algorithm with a multilevel paradigm, whereas the second uses the multiple ant colony algorithm as a refinement to the initial partition obtained by vector quantization. The two methods are experimentally compared with the well-known mesh-partitioning programs, p-METIS and Chaco.
We describe here a real case application of a formerly presented compression technique for the method of moments. This method is based on a QR compression of the impedance matrix off-diagonals blocks. In this letter, ...
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We describe here a real case application of a formerly presented compression technique for the method of moments. This method is based on a QR compression of the impedance matrix off-diagonals blocks. In this letter, it is extended to the multilevel three-dimensional case, and applied to the radiation of an antenna mounted on a car model. The ability of this technique to treat antenna radiation on a large complex structure is demonstrated, as well as the improvement in memory storage and computation time when. compared with the conventional method.
Spectral document clustering methods construct sparse word-document matrix W to measure the difference or similarity of documents. It may produce a dense similarity matrix S with W-T X W. We presented a multilevel alg...
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ISBN:
(纸本)1932415629
Spectral document clustering methods construct sparse word-document matrix W to measure the difference or similarity of documents. It may produce a dense similarity matrix S with W-T X W. We presented a multilevel algorithm on S in [9]. The spectral clustering algorithms on S work well when the size of the dataset is not too big. However, the multiplication for S takes too much time even with efficient sparse multiplication. In this paper, we present a variant of the algorithm on W and investigate two algorithms with computational experiments.
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